A344694 Numbers k, not powers of primes, for which A011772(k) divides A344875(k), and for all proper divisors d of k, A011772(d) < A011772(k).

900, 1260, 1560, 3740, 6552, 6669, 9680, 18981, 19880, 35784, 36080, 59040, 62238, 62244, 81872, 103730, 108500, 118910, 134420, 160160, 171740, 185724, 211072, 217833, 222224, 225929, 227528, 259325, 351072, 384944, 404294, 414778, 422604, 425178, 446600, 456228, 463008, 488205, 490105, 527100, 574308, 581184, 598400

Offset: 1

Author

Antti Karttunen, Jun 05 2021

Keywords

• nonn

Comments

Has many terms common with A344595.

Crossrefs

Cf. A011772, A344880, A344973.

Intersection of A024619, A344881 and A344974. Intersection of A344881 and A344975.

Cf. also A344595, A344980.

Programs

PARI

A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
A344880(n) = { my(x=A011772(n)); fordiv(n, d, if(A011772(d)==x, return(d==n))); };
A344973(n) = (A344875(n)%A011772(n));
isA344694(n) = ((n>1)&&!isprimepower(n)&&(0==A344973(n))&&A344880(n));